Textures on animated boolean moves with object
First start by making the texture "stay fixed" on the cylinder.  You can probably accomplish this by making a longer immobile cylinder which is then boolean intersected with a moving cube.  Then use that composite object to make the hole in the cube.

http://www.pasteall.org/blend/31488

The sample blend illustrates this.  

http://wiki.blender.org/index.php/Doc:2.6/Manual/Modifiers/Generate/Booleans#Materials documents that any new faces created in the process use the first material slot in the object hosting the modifier.  You will notice the cube has two materials.

You will notice that I have hide_render=True (the camera icon is greyed out in the outliner) for the drill objects.

The immobile drill cylinder has a UV map I created by marking seams and unwrapping with a cylindrical projection.